README.md

---
language: ab
language_name: Abkhazian
language_family: caucasian_northwest
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - feature-extraction
  - sentence-similarity
  - tokenization
  - n-grams
  - markov-chain
  - text-mining
  - fasttext
  - babelvec
  - vocabulous
  - vocabulary
  - monolingual
  - family-caucasian_northwest
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 4.193
  - name: best_isotropy
    type: isotropy
    value: 0.8394
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

# Abkhazian - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Abkhazian** Wikipedia data.
We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.

## 📋 Repository Contents

### Models & Assets

- Tokenizers (8k, 16k, 32k, 64k)
- N-gram models (2, 3, 4, 5-gram)
- Markov chains (context of 1, 2, 3, 4 and 5)
- Subword N-gram and Markov chains
- Embeddings in various sizes and dimensions (aligned and unaligned)
- Language Vocabulary
- Language Statistics

![Performance Dashboard](visualizations/performance_dashboard.png)

### Analysis and Evaluation

- [1. Tokenizer Evaluation](#1-tokenizer-evaluation)
- [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)
- [3. Markov Chain Evaluation](#3-markov-chain-evaluation)
- [4. Vocabulary Analysis](#4-vocabulary-analysis)
- [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)
- [6. Morphological Analysis (Experimental)](#6--morphological-analysis-experimental)
- [7. Summary & Recommendations](#7-summary--recommendations)
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
- [Visualizations Index](#visualizations-index)

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/tokenizer_compression.png)

![Tokenizer Fertility](visualizations/tokenizer_fertility.png)

![Tokenizer OOV](visualizations/tokenizer_oov.png)

![Total Tokens](visualizations/tokenizer_total_tokens.png)

### Results

| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|------------|-------------|---------------|----------|--------------|
| **8k** | 3.306x | 3.31 | 0.1493% | 223,032 |
| **16k** | 3.654x | 3.66 | 0.1650% | 201,823 |
| **32k** | 3.910x | 3.92 | 0.1766% | 188,563 |
| **64k** | 4.193x 🏆 | 4.20 | 0.1893% | 175,871 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ѳ, ѳ — кириллтәи аҩыратә архаикатә иажәхьоу нбан. Азхьарԥшқәа Graphemica (Ѳ) Gra...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ ѳ , ▁ ѳ ▁— ▁кириллтәи ▁аҩыратә ▁архаикатә ▁иажәхьоу ... (+11 more)` | 21 |
| 16k | `▁ѳ , ▁ѳ ▁— ▁кириллтәи ▁аҩыратә ▁архаикатә ▁иажәхьоу ▁нбан . ... (+9 more)` | 19 |
| 32k | `▁ѳ , ▁ѳ ▁— ▁кириллтәи ▁аҩыратә ▁архаикатә ▁иажәхьоу ▁нбан . ... (+9 more)` | 19 |
| 64k | `▁ѳ , ▁ѳ ▁— ▁кириллтәи ▁аҩыратә ▁архаикатә ▁иажәхьоу ▁нбан . ... (+9 more)` | 19 |

**Sample 2:** `Скуо-Уелли Winter Olympics, Jeux olympiques d'hiver de - аӡынтәи Олимпиадатә хәм...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁с ку о - у елли ▁winter ▁olympics , ▁jeux ... (+12 more)` | 22 |
| 16k | `▁с ку о - у елли ▁winter ▁olympics , ▁jeux ... (+12 more)` | 22 |
| 32k | `▁с ку о - уелли ▁winter ▁olympics , ▁jeux ▁olympiques ... (+11 more)` | 21 |
| 64k | `▁скуо - уелли ▁winter ▁olympics , ▁jeux ▁olympiques ▁d ' ... (+9 more)` | 19 |

**Sample 3:** `Ж, ж — кириллтәи аҩыратә нбан. Азхьарԥшқәа Graphemica (Ж) Graphemica (ж)`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ж , ▁ж ▁— ▁кириллтәи ▁аҩыратә ▁нбан . ▁азхьарԥшқәа ▁graphemica ... (+7 more)` | 17 |
| 16k | `▁ж , ▁ж ▁— ▁кириллтәи ▁аҩыратә ▁нбан . ▁азхьарԥшқәа ▁graphemica ... (+7 more)` | 17 |
| 32k | `▁ж , ▁ж ▁— ▁кириллтәи ▁аҩыратә ▁нбан . ▁азхьарԥшқәа ▁graphemica ... (+7 more)` | 17 |
| 64k | `▁ж , ▁ж ▁— ▁кириллтәи ▁аҩыратә ▁нбан . ▁азхьарԥшқәа ▁graphemica ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 4.193x compression
- **Lowest UNK Rate:** 8k with 0.1493% unknown tokens
- **Trade-off:** Larger vocabularies improve compression but increase model size
- **Recommendation:** 32k vocabulary provides optimal balance for production use

---
## 2. N-gram Model Evaluation

![N-gram Perplexity](visualizations/ngram_perplexity.png)

![N-gram Unique](visualizations/ngram_unique.png)

![N-gram Coverage](visualizations/ngram_coverage.png)

### Results

| N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|---------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | Word | 723 | 9.50 | 5,814 | 51.5% | 72.0% |
| **2-gram** | Subword | 363 | 8.51 | 4,117 | 60.3% | 96.8% |
| **3-gram** | Word | 252 | 7.98 | 5,218 | 66.6% | 80.6% |
| **3-gram** | Subword | 2,678 | 11.39 | 28,284 | 28.1% | 67.5% |
| **4-gram** | Word | 341 | 8.41 | 9,794 | 64.0% | 74.0% |
| **4-gram** | Subword | 11,104 | 13.44 | 112,814 | 16.8% | 44.7% |
| **5-gram** | Word | 198 🏆 | 7.63 | 7,301 | 69.5% | 78.6% |
| **5-gram** | Subword | 26,131 | 14.67 | 211,528 | 13.8% | 34.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `рыԥсҭазаара иалҵит` | 3,971 |
| 2 | `иит рыԥсҭазаара` | 3,938 |
| 3 | `рашәарамза ԥхынгәымза` | 3,603 |
| 4 | `жәабранмза хәажәкырамза` | 3,603 |
| 5 | `цәыббрамза жьҭаарамза` | 3,602 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `иит рыԥсҭазаара иалҵит` | 3,938 |
| 2 | `цәыббрамза жьҭаарамза абҵарамза` | 3,602 |
| 3 | `нанҳәамза цәыббрамза жьҭаарамза` | 3,601 |
| 4 | `жьҭаарамза абҵарамза ԥхынҷкәынмза` | 3,601 |
| 5 | `лаҵарамза рашәарамза ԥхынгәымза` | 3,601 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `цәыббрамза жьҭаарамза абҵарамза ԥхынҷкәынмза` | 3,601 |
| 2 | `нанҳәамза цәыббрамза жьҭаарамза абҵарамза` | 3,601 |
| 3 | `ԥхынгәымза нанҳәамза цәыббрамза жьҭаарамза` | 3,601 |
| 4 | `мшаԥымза лаҵарамза рашәарамза ԥхынгәымза` | 3,601 |
| 5 | `лаҵарамза рашәарамза ԥхынгәымза нанҳәамза` | 3,601 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `мшаԥымза лаҵарамза рашәарамза ԥхынгәымза нанҳәамза` | 3,601 |
| 2 | `рашәарамза ԥхынгәымза нанҳәамза цәыббрамза жьҭаарамза` | 3,601 |
| 3 | `ԥхынгәымза нанҳәамза цәыббрамза жьҭаарамза абҵарамза` | 3,601 |
| 4 | `нанҳәамза цәыббрамза жьҭаарамза абҵарамза ԥхынҷкәынмза` | 3,601 |
| 5 | `лаҵарамза рашәарамза ԥхынгәымза нанҳәамза цәыббрамза` | 3,601 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 154,936 |
| 2 | `_ а` | 150,057 |
| 3 | `р а` | 100,657 |
| 4 | `а р` | 84,729 |
| 5 | `ә а` | 76,114 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а р а` | 50,339 |
| 2 | `м з а` | 45,875 |
| 3 | `з а _` | 44,872 |
| 4 | `а _ а` | 35,534 |
| 5 | `а м з` | 31,361 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `м з а _` | 44,438 |
| 2 | `а м з а` | 30,790 |
| 3 | `р а м з` | 22,745 |
| 4 | `а р а _` | 19,530 |
| 5 | `қ ә а _` | 17,562 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а м з а _` | 29,604 |
| 2 | `р а м з а` | 22,366 |
| 3 | `а р а м з` | 15,138 |
| 4 | `т ә и _ а` | 11,926 |
| 5 | `а қ ә а _` | 9,350 |


### Key Findings

- **Best Perplexity:** 5-gram (word) with 198
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~34% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Contexts](visualizations/markov_contexts.png)

![Markov Branching](visualizations/markov_branching.png)

### Results

| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | Word | 0.6658 | 1.586 | 3.61 | 90,782 | 33.4% |
| **1** | Subword | 1.3353 | 2.523 | 10.79 | 879 | 0.0% |
| **2** | Word | 0.1206 | 1.087 | 1.22 | 327,437 | 87.9% |
| **2** | Subword | 1.0094 | 2.013 | 5.94 | 9,477 | 0.0% |
| **3** | Word | 0.0294 | 1.021 | 1.04 | 397,532 | 97.1% |
| **3** | Subword | 0.7766 | 1.713 | 3.69 | 56,288 | 22.3% |
| **4** | Word | 0.0100 🏆 | 1.007 | 1.01 | 413,065 | 99.0% |
| **4** | Subword | 0.5281 | 1.442 | 2.33 | 207,598 | 47.2% |

### Generated Text Samples (Word-based)

Below are text samples generated from each word-based Markov chain model:

**Context Size 1:**

1. `уи зыхҟьаз зеиҧш дыҟамыз аҧҳәызба ссир иргылеит еидҵоу қырҭтәыла адемократиатә хдырра асоциалтә хьча...`
2. `рыԥсҭазаара иалҵит пиотр актәи амаӡаныҟәгаҩыс ш вуковар vukovar jedna prica ш азхьарԥшқәа heritagesi...`
3. `иит рыԥсҭазаара иалҵит кринагор абырзен бызшәа афранцыз италиа иалаигалоит флоренцианӡагьы инеиуеит ...`

**Context Size 2:**

1. `иит рыԥсҭазаара иалҵит октавиан август аԥеиԥа диит ҳ ҟ 326 мцхеҭа ҳ ҟ 14 ш абанктә система`
2. `жәабранмза хәажәкырамза мшаԥымза лаҵарамза рашәарамза ԥхынгәымза нанҳәамза цәыббрамза жьҭаарамза абҵ...`
3. `рашәарамза ԥхынгәымза нанҳәамза цәыббрамза жьҭаарамза абҵарамза ԥхынҷкәынмза иит рыԥсҭазаара иалҵит ...`

**Context Size 3:**

1. `цәыббрамза жьҭаарамза абҵарамза ԥхынҷкәынмза иит рыԥсҭазаара иалҵит аныҳәақәа араԥтә ар амш аҳәаахьч...`
2. `жьҭаарамза абҵарамза ԥхынҷкәынмза иит рыԥсҭазаара иалҵит аныҳәақәа араԥтә ар амш аҳәаахьчаҩцәа рамш ...`
3. `ажьырныҳәамза жәабранмза хәажәкырамза мшаԥымза лаҵарамза рашәарамза ԥхынгәымза нанҳәамза цәыббрамза ...`

**Context Size 4:**

1. `цәыббрамза жьҭаарамза абҵарамза ԥхынҷкәынмза иит рыԥсҭазаара иалҵит клавдиа пульхра римтәи аамсҭаԥхә...`
2. `лаҵарамза рашәарамза ԥхынгәымза нанҳәамза цәыббрамза жьҭаарамза абҵарамза ԥхынҷкәынмза иит рыԥсҭазаа...`
3. `ԥхынгәымза нанҳәамза цәыббрамза жьҭаарамза абҵарамза ԥхынҷкәынмза иит рыԥсҭазаара иалҵит клавдиа пул...`


### Generated Text Samples (Subword-based)

Below are text samples generated from each subword-based Markov chain model:

**Context Size 1:**

1. `аякарамаҟәаҿы_«п`
2. `_жьы_ажәынқәсп_и`
3. `иха_аббарран._ло`

**Context Size 2:**

1. `а_уи_ахьы_иркую_с`
2. `_ареит._ара_ихьам`
3. `рала_ԥхын,_хьшара`

**Context Size 3:**

1. `араҟнытә_бызшәалеи`
2. `мза_жьҭаарамза_жәа`
3. `за_ԥхынгәырый_фано`

**Context Size 4:**

1. `мза_ракәзар,_зныз_х`
2. `амза_рашәара,_шықәс`
3. `рамза_ԥхынгәымза_ла`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (207,598 contexts)
- **Recommendation:** Context-3 or Context-4 for text generation

---
## 4. Vocabulary Analysis

![Zipf's Law](visualizations/zipf_law.png)

![Top Words](visualizations/top20_words.png)

![Coverage Curve](visualizations/vocab_coverage.png)

### Statistics

| Metric | Value |
|--------|-------|
| Vocabulary Size | 32,744 |
| Total Tokens | 441,086 |
| Mean Frequency | 13.47 |
| Median Frequency | 3 |
| Frequency Std Dev | 100.78 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | уи | 4,161 |
| 2 | рыԥсҭазаара | 4,025 |
| 3 | иит | 3,987 |
| 4 | иалҵит | 3,980 |
| 5 | лаҵарамза | 3,752 |
| 6 | жәабранмза | 3,722 |
| 7 | хәажәкырамза | 3,702 |
| 8 | абҵарамза | 3,701 |
| 9 | нанҳәамза | 3,696 |
| 10 | ԥхынҷкәынмза | 3,696 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | sons | 2 |
| 2 | extended | 2 |
| 3 | stream | 2 |
| 4 | block | 2 |
| 5 | stru | 2 |
| 6 | compressed | 2 |
| 7 | deflate | 2 |
| 8 | january | 2 |
| 9 | видеохәмарроуп | 2 |
| 10 | роблокс | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9626 |
| R² (Goodness of Fit) | 0.995444 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 30.3% |
| Top 1,000 | 55.7% |
| Top 5,000 | 76.9% |
| Top 10,000 | 85.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9954 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 30.3% of corpus
- **Long Tail:** 22,744 words needed for remaining 14.3% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.8394 | 0.3485 | N/A | N/A |
| **mono_64d** | 64 | 0.5679 | 0.2942 | N/A | N/A |
| **mono_128d** | 128 | 0.1636 | 0.2836 | N/A | N/A |
| **aligned_32d** | 32 | 0.8394 🏆 | 0.3421 | 0.0220 | 0.1360 |
| **aligned_64d** | 64 | 0.5679 | 0.2946 | 0.0360 | 0.1960 |
| **aligned_128d** | 128 | 0.1636 | 0.2850 | 0.0420 | 0.2180 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8394 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3080. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.2% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **2.615** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **1.280** | High formulaic/idiomatic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-иа` | иалаҵоу, иааргазар, иадлоит |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | акандидатцәа, азура, ашәара |
| `-әа` | акандидатцәа, акрақәа, аконсультациақәа |
| `-ит` | иҟамлеит, дагәыланахалоит, дашьҭалоит |
| `-қәа` | акрақәа, аконсультациақәа, дунеихәаԥшрақәа |
| `-ра` | азура, ашәара, рықәцара |
| `-тә` | алашаратә, аҵакырадгьылтә, аетнографиатә |
| `-еи` | ргәыԥқәеи, астатуиақәеи, аизгақәеи |
| `-еит` | иҟамлеит, ԥхасҭахеит, игәарҭеит |

### 6.3 Bound Stems (Lexical Roots)

Bound stems are high-frequency subword units that are semantically cohesive but rarely appear as standalone words. These often correspond to the 'core' of a word that requires inflection or derivation to be valid.

| Stem | Cohesion | Substitutability | Examples |
|------|----------|------------------|----------|
| `гыла` | 1.73x | 82 contexts | гылан, ргылан, дгылан |
| `ықәс` | 1.84x | 26 contexts | шықәс, щықәса, ашықәс |
| `әыла` | 1.68x | 34 contexts | тәыла, тәылак, ртәыла |
| `аҵар` | 1.63x | 38 contexts | аҵара, лаҵара, аҵареи |
| `қәса` | 1.96x | 16 contexts | щықәса, шықәса, шиқәсазы |
| `арам` | 1.86x | 17 contexts | харам, нарам, гуарам |
| `азаа` | 1.69x | 23 contexts | лазаа, амазаап, иазааит |
| `әара` | 1.30x | 58 contexts | шәара, акәара, ҿҳәара |
| `ҭаза` | 2.37x | 8 contexts | иԥсҭазара, ԥсҭазаара, иԥсҭазаара |
| `шәар` | 1.56x | 26 contexts | шәара, шәарах, ашәара |
| `заар` | 2.09x | 10 contexts | акзаара, аҟазаара, акзаареи |
| `ыҳәа` | 1.57x | 22 contexts | ныҳәа, рныҳәа, иныҳәа |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-иа` | `-ит` | 83 words | иаабоит, иацхраауеит |
| `-иа` | `-еит` | 50 words | иацхраауеит, иартәеит |
| `-иа` | `-а` | 43 words | ианырба, ианрылага |
| `-иа` | `-әа` | 11 words | иацәыхарамкәа, иаламлакәа |
| `-иа` | `-тә` | 5 words | иааникыларатә, иавтобиографиатә |
| `-иа` | `-ра` | 3 words | иавторра, иамхра |
| `-иа` | `-еи` | 2 words | ианԥсеи, иашьцәеи |
| `-иа` | `-қәа` | 2 words | иажәақәа, иажәамаанақәа |
| `-иа` | `-ақәа` | 1 words | иажәақәа, иажәамаанақәа |

### 6.5 Recursive Morpheme Segmentation

Using **Recursive Hierarchical Substitutability**, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., `prefix-prefix-root-suffix`).

| Word | Suggested Split | Confidence | Stem |
|------|-----------------|------------|------|
| анхарҭатә | **`анхарҭа-тә`** | 4.5 | `анхарҭа` |
| рхыԥхьаӡараҟнытә | **`рхыԥхьаӡараҟны-тә`** | 4.5 | `рхыԥхьаӡараҟны` |
| аӡхықәқәа | **`аӡхықә-қәа`** | 4.5 | `аӡхықә` |
| астуденттә | **`астудент-тә`** | 4.5 | `астудент` |
| аҳәынҭқарқәа | **`аҳәынҭқар-қәа`** | 4.5 | `аҳәынҭқар` |
| каталониатә | **`каталониа-тә`** | 4.5 | `каталониа` |
| абиблиографиатә | **`абиблиографиа-тә`** | 4.5 | `абиблиографиа` |
| аредакциатә | **`аредакциа-тә`** | 4.5 | `аредакциа` |
| амилициатә | **`амилициа-тә`** | 4.5 | `амилициа` |
| амилаҭқәа | **`амилаҭ-қәа`** | 4.5 | `амилаҭ` |
| аекологиатә | **`аекологиа-тә`** | 4.5 | `аекологиа` |
| адемографиатә | **`адемографиа-тә`** | 4.5 | `адемографиа` |
| аконсервациатә | **`аконсервациа-тә`** | 4.5 | `аконсервациа` |
| ауаҩытәыҩсатә | **`ауаҩытәыҩса-тә`** | 4.5 | `ауаҩытәыҩса` |
| аелементқәа | **`аелемент-қәа`** | 4.5 | `аелемент` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Abkhazian shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.19x) |
| N-gram | **5-gram** | Lowest perplexity (198) |
| Markov | **Context-4** | Highest predictability (99.0%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-03 16:16:58*